Detection and computation of conservative kernels of models consisting of freeform curves and surfaces, using inequality constraints.

• An algorithm to compute a conservative approximation of the kernel of freeform curves and surfaces is presented. • Inequality constraints for the interior of kernel domains are formulated and solved using a subdivision-based approach. • The proposed algorithm computes the kernel of various freeform curves and surfaces consisting of multiple, C 1 -discontinuous, and/or open curves and surfaces. We present an algorithm to compute a tight-as-needed conservative approximation of the kernel domain of freeform curves in R 2 and freeform surfaces in R 3. Inequality constraints to detect the interior of the kernel domain are formulated as multivariates, and solved with a subdivision-based approach to find the domains in R 2 or R 3 that satisfy the inequalities and are in the kernel. The convex hull of the computed domains is also included in the kernel, and adopted as the approximated kernel domain. We can apply the presented algorithm to detect the kernel domain of not only C 1 continuous closed regular curves and surfaces, but also the kernel domains of multiple piecewise C 1 continuous regular freeform curves and surfaces. Further, the presented algorithm can be applied to find the gamma-kernel as well as the kernel domain of open curves and surfaces, under some assumptions. We demonstrate our experimental result using various freeform curves and surfaces, and compare it with the kernel computation algorithm presented in Elber et al. (2006). [ABSTRACT FROM AUTHOR]